Dans cette note exploratoire, nous proposons d’explorer la base CHELEM du CEPII à l’aide de la grille d’agrégation des pays du monde VERTICALES mise au point à partir des idées de Jean-Louis Guigou et des chercheurs de l’IPEMED. Le découpage proposé est organisé à deux niveaux, en 4 régions (VER1) elle-mêmes subdivisées en 12 sous-régions (VER2).
La base CHELEM, même si elle offre une résolution spatiale moindre que d’autres bases (94 états ou groupes d’états) permet de décomposer les échanges par type de produit ce qui permet de mettre à jour différentes formes de régionalisation en fonction des produits concernés.
L’idée de base est de proposer une lecture du Monde à partir de 4 régions “verticales” disposées du Nord au Sud. Trois de ces régions ont déjà été souvent analysées par les chercheurs de l’IPEMED. Mais nous avons jugé intéressant de rajouter une 4e région correspondant au “reste du Monde”.
La base CHELEM a réussi l’exploit de constituer une catégorisation des produits échangés sur plus de 50 ans malgré l’évolution des types de production et les changements de nomenclature. Nous adoptons ici une version simplifié de cette classification en 9 familles de produits correspondant à différents niveaux d’insertion dans les chaînes de valeur et la division internationale du travail (Grasland and Van Hamme (2010), Grataloup, Boucheron, and Fumey (2014))
Quelques rattachements non voulus ont par ailleurs été imposés par la structure de la base CHELEM du fait de l’existence d’agrégats de pays non séparables (e.g. rattachement de l’Afghanistan à l’ensemble Asie-Pacifique ou du Yemen à l’ensemble Europe-Méditerranée-Afriqe)
La quatrième région “reste du Monde” n’est pas a priori une zone d’intégration régionale mais elle doit être prise en compte pour compléter l’analyse et lui donner une dimension globale. Elle comporte des pays qui sont tiraillés entre plusieurs orientations régionales à l’instar de la Russie, L’Inde ou l’Arabie Saoudite.
Dans cette première partie on procède à une synthèse rapide des échanges commerciaux entre les quatres grandes régions afin de déterminer la part du commerce interne à chacune de celles-ci, puisles variations de l’intégration régionale par produit et enfin par région.
Commentaires :
L’analyse des exportations montre une forte intégration de la région Europe-Méditerranée Afrique tout au long de la période mais avec une tendance à la baisse dans les années 2000 et une stabilisation actuelle autour de 70% en 2020. Dans le cas des Amériques, l’intégration avait fortement augmenté dans les années 1990 avant de redescendre pour se stabiliser autour de 50% en 2020. La région Asie-Pacifique part d’une faible intégration dans les années 1970-1980 mais enregistre ensuitre des progrès continus pour atteindre presque 50% en 2020
L’analyse des importations montre une évolution assez similaire à celle des exportations dans le cas de la région Europe-Méditerranée-Afrique pour aboutir également à un niveau de 70%. La situation est très différente dans les deux autres régions du Monde car on assiste à une baisse continue de l’intégration des Amériques (moins de 40% en 2020) et une hausse continue de celle-ci dans la région Asie-Pacifique (presque 60% en 2020).
Il faut toutefois noter que le maintien d’une forte intégration de la région Europe-Méditerranée-Afrique est en grande partie liée aux échanges internes à la seule Union Européenne et pas nécessairement aux échanges Nord-Sud entre l’Europe et la méditerranée ou l’Europe et l’Afrique. Il est donc nécessaire de regarder plus en détail les échanges de chaque pays ou agrégat de pays avec les trois grandes régions du Monde
On peut imaginer une autre lecture centrée sur la division du Monde entre pays du Nord et pays du Sud. Mais cela impose de choisir une typologie qui est par définition évolutive au cours du temps.
[1] "BRICS-BRICS" "BRICS-Nord" "BRICS-Sud" "Nord-BRICS" "Nord-Nord"
[6] "Nord-Sud" "Sud-BRICS" "Sud-Nord" "Sud-Sud"
Nous analysons ici la validité du découpage du monde en trois verticales en procédant à une évaluation de la part des échanges de chaque pays ou agrégat de pays vers les trois régions postulées par J.L. Guigou oui vers la région résiduelle “reste du monde”. On considère trois situations possibles :
Nous présentons les cartes de régionalisation importations et exportations pour deux périodes décennales : en 1991-2000 et en 2011-2020
La région Europe-Méditerranée-Afrique demeure bien intégrée en matière d’exportations dans sa partie européenne et méditerranéenne puisque tous les pays y affichent des exportations destinées à plus de 50% vers la verticale, exception faite des pays du levant (Syrie, Liban, Israël, Jordanie). Mais la situation est désormais plus constrastée en Afrique subsaharienne où l’intégration est forte pour le Cameroun, la Côte d’Ivoire et le Kénya, mais faible pour le Ghana, le Nigéria, le Congo et l’Afrique australe. Quant aux autres pays ils dirigent leurs exportations en priorité vers la région Asie Pacifique même si l’intégration y demeure assez faible (40-50%) sauf dans le cas du Gabon.
La région Amériques demeur également bien intégrée en matière d’exportations, notamment dans sa partie septentrionale (Canada, Mexique, Amérique centrale, Colombie, Venezuela). Mais on retrouve comme en 1991-2000 une intégration plus faible des USA (qui exportent beaucoup en dehors de leur région) et de l’Argentine. Le Chili apparaît quant à lui davantage tourné vers l’Asie Pacifique tandis que le Brésil montre désormais une part égale d’exportations (34%) vers les Amériques et l’Asie-Pacifique.
La région Asie-Pacifique polarise beaucoup plus fortement qu’en 1991-2000 son espace interne mais aussi l’ensemble des pays du Golfe Persique qui assurent son approvisionnement en hydrocarbure ainsi que le Gabon. Elle polarise faiblement une partie de l’Afrique subsaharienne et le Chili. La Chine apparait la moins intégrée du fait du déploiement de ses relations au niveau mondial plutôt qu’à l’intérieur de la seule région Asie-Pacifique. Elle envoie approximativement autant vers l’Asie-Pacifique (31%) , Les Amériques (30%) et l’Europe-Méditerranée-Afrique (26%).
L’Inde quant à elle maintient une position de struct équilibre entre les quatre régions du Monde, envoyant de 20 à 30% vers chacune d’entre elles.
Nous procédons maintenant à une analyse plus détaillée des relations entre les 12 sous-régions afin de vérifier si les liens observés au niveau macroscopiques sont confirmés au niveau infra-régional. Pour cela, nous allons confronter les flux observés entre pays à ceux qui seraient obtenus dans l’hypothèse d’un modèle aléatoire d’indifférence à la distance.
- Commentaire: La montée en puissance de la Chine accentue la polarisation du Monde entre trois régions et s’accompagne d’un éloignement de plus important de l’Afrique par rapport à l’Europe. L’Asie du Sud et les pays du Golfe basculent dans la zone d’échange préférentiels de l’Asie. Les Amériques maintiennent des échanges préférentiels mais subissent l’influence croissante et asymétrique de l’Asie pacifique qui exporte vers eux mais n’importe guère. Le déficit commercial des USA par rapport à la Chine se creuse de plus en plus.
- Commentaire: L’Asie de l’Est constitue désormais l’acteur majeur du commerce mondial et inclue dans sa zone d’échanges préfrentiels non seulement l’Asie du Sud et les pays du Golfe mais aussi l’Afrique subsaharienne et peut-être l’Amérique du Sud. Les relations préférentielles de l’Europe se limitent à elle-même ainsi que ses voisins les plus proches à l’Est et au Sud. Même chose pour les Amériques où l’intégration concerne désormais surtout la partie septentrionale et centrale.
This working paper propose to discuss the theoretical problem of regionalisation of a world (in abstract sense) through the empirical example of The World (where we live) described by trade flows over a long period of time and for different types of products.
We will use for that purpose the CHELEM database produced by the CEPII which offers an exceptional coverage of trade flows over a period of 50 years from 1967 to present (2020). The most detailed version of this database describes the exchange between 94 x 94 territorial units (states or group of states) for 72 types of goods over a period of 54 years which means a 4-dimension object (hypercube) of size \(94 \times 93 \times 72 \times 54 = 33988896\) cells.
For our experiment, we will use a reduction of the database based on 12 territorial units described by 9 groups of goods for 5 periods of 10 years each. The hypercube used in our experiment will be therefore limited to a size of \(12 \times 11 \times 9 \times 5 = 5940\) cells. This can appear rather limited but - as we will demonstrate - the complexity of such an object is yet very high and it appears better to establish the theoretical foundation of the research of such an object before to adress larger databases where computational problem will grow exponentially.
Our overarching question can now be formulated in the following way :
Let \(W\) be a world divided in \(1\dots i\dots n\) territorial units.
Let \(F\) a relation defined on \(W \times W\) which assign a value to each couple of units of the world (excluding only internal relations).
Let \(X\) a typology of relations in \(1\dots k\dots p\) types of relation using the same unit of mesurement.
Let \(T\) a partition of time in periods \(1\dots t\dots q\) where the relations are measured
Let \(H = F_{ijkt}\) the hypercube which measure of relation between territorial units \(i\) and \(j\) for the relation \(k\) during time period \(t\)
Problem 1 : What are the partitions \(P_i\) (for origins), \(P_j\) (for destination), \(P_k\) (for typology) and \(P_t\) (for time period) that allows to reduce the size of the initial hypercube \(H\) to a smaller one \(H'\) without losing too much information.
Problem 2 : can we identify homogeneous subparts of \(H\) that are not necessarily based on orthogonal divisions of the hypercube.
Problem 3: can we identify trajectories of regionalisation \(P_i(t)\), \(P_j(j)\) or trajectories of typology \(P_k(t)\) that descibe the evolution of optimal partitions through time .
The original version of the CHELEM database is made of 94 territorial units. A majority of this territorial units correspond to states but some of them are made of aggregates of states for which it was difficult to separate trade flows or to collect them. The map below indicates what are the territorial units that do not fit with international division of the world in states.
The aggregates of states are generally based on groups of small states (like in central America or Oceania) but it can also be the case for larger goups of states playing an important role in trade like in the case of the aggregate between Irag, Iran and Koweit. The aggregation is also very large in the case of subsaharan Africa where only few states are identified and the other mixed in large area, not necessarily contiguous. At the same time, Europe is fully disaggregated in isolated states, except in the case of Malta and Cyprus, which will have for consequence an increase of trade flows in this part of the world. if USA was divided in 51 federal states and China or India in provinces or states, it would necessarily increase their part of exchanges.
We are therefore facing here a difficult question of Modifiable Area Unit Problem (MAUP) which can not be easily solved without deciding immediately to aggregate the data in larger units, more homogeneous, where internal flows will be systematically removed. This will produce of course a strong reduction of the initial information but make possible to have a better analysis of the relation between the new territorial units.
On the basis of expert advices, we have chosen 12 basic territorial units which are in fact associated to a first division of the world in 4 regions, each of them divided in 3 subregions.
The autors of this partition of the world suggest that the world economy has been (at least during a period of time) or could have been (whishfull thinking ?) be organized around three integrated “vertical macroregions” and one residual part of the word less integrated and submit to variable influence of the three vertical regions :
G1 : Europe-Mediterranea-Africa : Clearly inherited from the history, this vertical region is based on various type of proximities including geographical distance, common sea (Mare Nostrum), common language, colonial legacy … But what has been the destiny of these links over the last 50 years following the independancy of states from Africa ?
G2 : Americas : Since the 19th century, “the Monroe Doctrine is a United States foreign policy position that opposes European colonialism in the Western Hemisphere. It holds that any intervention in the political affairs of the Americas by foreign powers is a potentially hostile act against the United States” (Wikipedia). This doctrine has been related to lot of conflict between the different parts of Americas but also associated to the building of various forms of cooperation like NAFTA (1994), MERCOSUR (1991), etc… In any case, the geographical proximity was clearly here in favor of a potential integration. But the reduction of transport cost in the 1980’s has modified the role played by these factor in favor of trans-Pacific relationships. So, what is the situation of America’s integration over our 50 years period of interest ?
G3 : Asia-Pacifica : The economic integration of this part of the world is a long and complex process initially boosted by Japan and Korea, further by China and associated to a continuous process or development of free trade areas like ASEAN. This potential macro-region has been at the same time the pivot of global economic integration of the world, firstly with trans-pacific relation until 1990 and further with the rest of the world with the growing influence of China after this state joined the WTO in 2001. So, is it still a macroregion or the economic core of contemporary world ?
G4 : Rest of the World : We can not speak here from an integrated economic region but rather as a group of states that (1) benefit from ressources of interest forthe rest of the world (e.g. oil and gas from the Gulf, mineral products from Russia, …) and/or (2) develop a strategy of diversification of their exchange at world scale and refuse to be dependent from too powerful partners (e.g. strategy of India, Russia or Saudi Arabia). The question here is to what extent this part of the world remained “neutral” as compare to the three other ones or has been succesfully associated to the different other regions according to variable geometries.
All this remarks are hypothesis that suggest a possible way to cluster the 12 territorial units in 3 or four groups. But our aim is not here to validate the partition \((G_1,G_2,G_3,G_4)\) but rather to use it at starting point for the discovery of alternative geometries changing throug time or presenting variable configurations according to the type of products considered.
The authors of the database CHELEM as made incredible efforts to maintain an homogeneous categorisation of goods in 72 types of producst over a period of 50 years. Considering the changes of the world economy and the evolution of the nomenclature used by trade organization, it is a genuine miracle to have done such a work. We adopt here a simplified version of the CHELEM typology in only 9 groups of products that reflect the distribution of value chains as well as the international division of labor (Grasland and Van Hamme (2010), Grataloup, Boucheron, and Fumey (2014))
On the basis of previous rules we have built the expected hypercube with 5940 cells. The flows has been normalized to an arbitrary total sum of 1000000 for each period of ten years and the values has been round with zero decimal. We have introduced for each couple of region the flows in both direction \(F_{ijkt}\) and \(F_{jikt}\) in order to be able to compute easily the symetric part of exchange called volume and the asymetric part called balance :
| i | j | k | t | Fijkt | Fjikt | Vijkt | Bijkt |
|---|---|---|---|---|---|---|---|
| G11:Europe | G12:Medit.SE | (1) ENE | 1971-80 | 1239 | 16658 | 8948 | -15419 |
| G11:Europe | G12:Medit.SE | (1) ENE | 1981-90 | 904 | 16290 | 8597 | -15386 |
| G11:Europe | G12:Medit.SE | (1) ENE | 1991-00 | 652 | 8143 | 4398 | -7490 |
| G11:Europe | G12:Medit.SE | (1) ENE | 2001-10 | 1371 | 9031 | 5201 | -7660 |
| G11:Europe | G12:Medit.SE | (1) ENE | 2011-20 | 1942 | 5057 | 3499 | -3115 |
| G11:Europe | G12:Medit.SE | (2) MIN | 1971-80 | 3849 | 1489 | 2669 | 2361 |
| G11:Europe | G12:Medit.SE | (2) MIN | 1981-90 | 3196 | 1187 | 2192 | 2009 |
| G11:Europe | G12:Medit.SE | (2) MIN | 1991-00 | 2234 | 875 | 1554 | 1359 |
| G11:Europe | G12:Medit.SE | (2) MIN | 2001-10 | 2188 | 1169 | 1679 | 1019 |
| G11:Europe | G12:Medit.SE | (2) MIN | 2011-20 | 1978 | 936 | 1457 | 1042 |
Before to adress the problem of research of an unknown partition, we will discuss the question of measuring the accuracy of an existing partition, which will help us to precise the problem of the choice of an optimisation criteria.
We will take as example the bilateral trade flows (\(V_ijkt\)) in order to have the same partition for origins and destination (the problem of asymmetry will be discussed later) and consider the total sum of flows in 1991-2000 as starting example. The existing partition will be the division in 4 regions (3 verticales + 1 residual).
| G11 | G12 | G13 | G21 | G22 | G23 | G31 | G32 | G33 | G41 | G42 | G43 | Sum | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| G11 | 0 | 24373 | 11640 | 64562 | 5708 | 11391 | 50525 | 16925 | 4837 | 16958 | 11407 | 5747 | 224073 |
| G12 | 24373 | 0 | 455 | 5332 | 146 | 838 | 3061 | 864 | 220 | 1375 | 1521 | 566 | 38751 |
| G13 | 11640 | 455 | 0 | 4183 | 112 | 677 | 3995 | 893 | 197 | 175 | 561 | 853 | 23742 |
| G21 | 64562 | 5332 | 4183 | 0 | 33752 | 13169 | 73913 | 18473 | 4013 | 1748 | 5233 | 2960 | 227336 |
| G22 | 5708 | 146 | 112 | 33752 | 0 | 2459 | 4733 | 709 | 118 | 857 | 314 | 96 | 49003 |
| G23 | 11391 | 838 | 677 | 13169 | 2459 | 0 | 5105 | 926 | 226 | 372 | 774 | 339 | 36275 |
| G31 | 50525 | 3061 | 3995 | 73913 | 4733 | 5105 | 0 | 37009 | 8435 | 3648 | 13332 | 3444 | 207199 |
| G32 | 16925 | 864 | 893 | 18473 | 709 | 926 | 37009 | 0 | 3282 | 755 | 3671 | 1853 | 85360 |
| G33 | 4837 | 220 | 197 | 4013 | 118 | 226 | 8435 | 3282 | 0 | 46 | 558 | 382 | 22316 |
| G41 | 16958 | 1375 | 175 | 1748 | 857 | 372 | 3648 | 755 | 46 | 0 | 448 | 501 | 26882 |
| G42 | 11407 | 1521 | 561 | 5233 | 314 | 774 | 13332 | 3671 | 558 | 448 | 0 | 2252 | 40070 |
| G43 | 5747 | 566 | 853 | 2960 | 96 | 339 | 3444 | 1853 | 382 | 501 | 2252 | 0 | 18994 |
| Sum | 224073 | 38751 | 23742 | 227336 | 49003 | 36275 | 207199 | 85360 | 22316 | 26882 | 40070 | 18994 | 1000000 |
Assuming that flows are made of 1000000 of discrete events (the total sum of the matrix) we choose as reference (null model) a situation where the export \(O_i\) and import \(D_j\) of each spatial unit is known (margins of the matrix) and where the exchange are randomly distributed. Because of the absence of information on the diagonal of the matrix (trade internal to each region), the model can not be solved by a simple estimation but desserve an iterative double constraint model taking the from
\(F_{ij}^* = a_i.O_i.b_j.D_j+\epsilon_{ij}\)
Analysis of Deviance Table
Model: poisson, link: log
Response: Vij
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 131 2101056
i 11 815299 120 1285757 < 2.2e-16 ***
j 11 1014053 109 271704 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square = 0.871"
This first model account for 87% of the initial deviance of the model which is important but logical considering the inequal size of the territorial units in terms of trade volume.
The analysis of standardized residual make possible to visualize the couple of units where exchanges are higher or lower than expected. A classification of this matrix of residuals make possible to reveal a structure in “blocks” of units that has more internal exchanges than expected.
We notice here that the classification of residuals fit relatively nicely with the expectations of the experts as we can recognize on the diagonal two first groups corresponding to the region Asia-Pacifica \((G_{31},G_{32}, G_{33})\) and the region Americas \((G_{21},G_{22}, G_{23})\). But the next region is limited to only two members of the Rest of the world \((G_{43},G_{43})\) because Russia \((G41)\) seems to be more associated with the region Europe-Mediterranea-Africa \((G_{11},G_{12}, G_{13})\).
We can try to build a first regional model that assume the existence of a simple preference effect with the same value \(\gamma\) for units located inside the same region:
\(F_{ij}^* = a_i.O_i.b_j.D_j.\gamma^{REG}+\epsilon_{ij}\)
Despite the analysis made on the residuals, we decide to keep the partition in 4 regions forecast by the experts.
Analysis of Deviance Table
Model: poisson, link: log
Response: Vij
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 131 2101056
i 11 815299 120 1285757 < 2.2e-16 ***
j 11 1014053 109 271704 < 2.2e-16 ***
REG 1 160356 108 111348 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Total) = 0.947"
Analysis of Deviance Table
Model 1: Vij ~ i + j
Model 2: Vij ~ i + j + REG
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 109 271704
2 108 111348 1 160356 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Gain) = 0.59"
We obtain a model with a pseudo R-square equal to 95 % of deviance explianed (including the effect of the null model) or 59 % of residual deviance of the reference model (excluding therefore what has been yet explained by double constraint on origins and estination). The coefficient \(\gamma\) is very significant and equal to 3.02 which means that exchanges between units located in the same region are in average 3 times greater than exchanges between units located in different regions.
We can adopt a different perspective and imagine that they are as many value of the parameter \(\gamma_{k}\) as they are possibilities of belonging to the same regions. Our model wil therefore take the form
\(F_{ij}^* = a_i.O_i.b_j.D_j.\gamma_{k}^{REG_{k}}+\epsilon_{ij}\)
Analysis of Deviance Table
Model: poisson, link: log
Response: Vij
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 131 2101056
i 11 815299 120 1285757 < 2.2e-16 ***
j 11 1014053 109 271704 < 2.2e-16 ***
REG1 1 66272 108 205433 < 2.2e-16 ***
REG2 1 71893 107 133540 < 2.2e-16 ***
REG3 1 30040 106 103500 < 2.2e-16 ***
REG4 1 467 105 103034 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Total) = 0.951"
Analysis of Deviance Table
Model 1: Vij ~ i + j
Model 2: Vij ~ i + j + REG
Model 3: Vij ~ i + j + REG1 + REG2 + REG3 + REG4
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 109 271704
2 108 111348 1 160356 < 2.2e-16 ***
3 105 103034 3 8314 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Gain) = 0.621"
This model acount know for 95.1 % of the total deviance and 62.1% of the residual deviance of the reference model. It offers a significant improvement of the previous model and reveal that the levels of integration are different in each region. The most integrated regions are Europe_Mediterranea_Africa (\(\gamma_1=3.72\)) and Americas (\(\gamma_2=3.84\)),followed by Asia-Pacifica (\(\gamma_3=2.45\)) and finally the rest of the world (\(\gamma_4=1.36\))
In the previous analysis we have followed the expert advice concerning the division of the world in 4 regions. But we can ask if these choice was really optimal. Looking at the residual of the reference model, we can imagine another partition of the world in four groups where Russia is associated to the region Europe-Mediterranea-Asia. What would be the result ?
Analysis of Deviance Table
Model: poisson, link: log
Response: Vij
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 131 2101056
i 11 815299 120 1285757 < 2.2e-16 ***
j 11 1014053 109 271704 < 2.2e-16 ***
REG1 1 113899 108 157805 < 2.2e-16 ***
REG2 1 64655 107 93150 < 2.2e-16 ***
REG3 1 24385 106 68765 < 2.2e-16 ***
REG4 1 3706 105 65059 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Total) = 0.969"
Analysis of Deviance Table
Model 1: Vij ~ i + j
Model 2: Vij ~ i + j + REG
Model 3: Vij ~ i + j + REG1 + REG2 + REG3 + REG4
Model 4: Vij ~ i + j + REG1 + REG2 + REG3 + REG4
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 109 271704
2 108 111348 1 160356 < 2.2e-16 ***
3 105 103034 3 8314 < 2.2e-16 ***
4 105 65059 0 37975
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[1] "Mc Fadden Pseudo R-square (Gain) = 0.761"
This model acount now for 96.9 % of the total deviance and 76.1% of the residual deviance of the reference model. It offers a significant improvement of the previous model and modify the levels of integration each region. The integration of the Europe_Mediterranea_Africa extende to Russia is increased (\(\gamma_1=4.74\)) but a small decrease is observed in Americas (\(\gamma_2=3.54\)), in Asia-Pacifica (\(\gamma_3=2.24\)) but we observe a strong decrease of integration in the remaining part of the rest of the world (\(\gamma_4=3.1\)).
We decide know to replicate the model 2 for each of thetime period in order to examine the variations of regional integration.
Analysis of Deviance Table
Model: poisson, link: log
Response: Vijkt
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 5939 12089700
i:t 59 3362205 5880 8727495 < 2.2e-16 ***
t:j 55 4213874 5825 4513621 < 2.2e-16 ***
t:REG1 5 273136 5820 4240485 < 2.2e-16 ***
t:REG2 5 323063 5815 3917422 < 2.2e-16 ***
t:REG3 5 198226 5810 3719196 < 2.2e-16 ***
t:REG4 5 10156 5805 3709039 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| reg | 1971-80 | 1981-90 | 1991-00 | 2001-10 | 2011-20 | |
|---|---|---|---|---|---|---|
| Eur-Med-Afr | REG1 | 2.87 | 3.76 | 3.72 | 2.35 | 2.25 |
| Americas | REG2 | 3.03 | 2.88 | 3.84 | 4.50 | 4.49 |
| Asia-Pacifica | REG3 | 4.29 | 3.11 | 2.45 | 2.76 | 2.82 |
| Rest of the World | REG4 | 0.44 | 0.71 | 1.35 | 1.26 | 1.46 |
_ Commentaire : The introduction of time reveals variations of regional integration through time. For example, the region Eur-Med-Afr has a maximum integration in 1981-1990 and 1990-2000 but lower level before and after. The region Americas, on the contrary has a maximum integration in the final periods of 2001-2010 and 2011-2020. The region Asia-Pacifica was very integrated in 1971-80 and experiment a decrease until 1991-2000 before to increase slowly again.
Here, we replicate the model 2 but we examine separately the level of integration by products.
Analysis of Deviance Table
Model: poisson, link: log
Response: Vijkt
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 1187 2623295
i:k 107 1079780 1080 1543515 < 2.2e-16 ***
k:j 99 1174358 981 369157 < 2.2e-16 ***
k:REG1 9 68333 972 300825 < 2.2e-16 ***
k:REG2 9 91251 963 209573 < 2.2e-16 ***
k:REG3 9 44302 954 165271 < 2.2e-16 ***
k:REG4 9 4501 945 160770 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| reg | AGR | CHE | ELE | ENE | EQU | MIN | MIS | TEX | TRA | |
|---|---|---|---|---|---|---|---|---|---|---|
| Eur-Med-Afr | REG1 | 3.66 | 3.03 | 7.28 | 4.98 | 3.80 | 2.26 | 1.72 | 6.91 | 3.05 |
| Americas | REG2 | 1.72 | 3.57 | 7.39 | 16.81 | 3.64 | 2.37 | 10.16 | 6.76 | 2.20 |
| Asia-Pacifica | REG3 | 3.65 | 3.35 | 1.07 | 8.30 | 2.99 | 5.67 | 4.87 | 1.33 | 2.32 |
| Rest of the World | REG4 | 1.71 | 1.86 | 2.44 | 0.27 | 1.02 | 0.85 | 0.99 | 1.76 | 1.43 |
The sequence of models indicates that a simple validation of an existing partition does not guarantee that we have found the optimal solution. In our example, we should certainly explore all the possible partition before to validate our final model as the best partition of world trade in 4 regions.
We have also to consider that the decision fo choose 4 regions is not necessarily optimal and we could imagine that more interestin results could be achieved with a partition in 2, 3 or 5 regions. But in this case we have to propose a criterium of optimisation like AIC or BIC which take into account the number of classes used. Finally our results sggest:
In other words, the question of optimal regionalisation is very complex but also very exciting …
We propose here a different approach of the problem of regionalisation using a inverse gravity model for the extraction of trade distances and multidimensional scaling for the realisation of a map of relative position of world regions in a bi-dimensional space.
We start again from the matrix of trade flows between the 12 world subregions described in the previous part of the analysis.
| G11 | G12 | G13 | G21 | G22 | G23 | G31 | G32 | G33 | G41 | G42 | G43 | Sum | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| G11 | 0 | 24373 | 11640 | 64562 | 5708 | 11391 | 50525 | 16925 | 4837 | 16958 | 11407 | 5747 | 224073 |
| G12 | 24373 | 0 | 455 | 5332 | 146 | 838 | 3061 | 864 | 220 | 1375 | 1521 | 566 | 38751 |
| G13 | 11640 | 455 | 0 | 4183 | 112 | 677 | 3995 | 893 | 197 | 175 | 561 | 853 | 23742 |
| G21 | 64562 | 5332 | 4183 | 0 | 33752 | 13169 | 73913 | 18473 | 4013 | 1748 | 5233 | 2960 | 227336 |
| G22 | 5708 | 146 | 112 | 33752 | 0 | 2459 | 4733 | 709 | 118 | 857 | 314 | 96 | 49003 |
| G23 | 11391 | 838 | 677 | 13169 | 2459 | 0 | 5105 | 926 | 226 | 372 | 774 | 339 | 36275 |
| G31 | 50525 | 3061 | 3995 | 73913 | 4733 | 5105 | 0 | 37009 | 8435 | 3648 | 13332 | 3444 | 207199 |
| G32 | 16925 | 864 | 893 | 18473 | 709 | 926 | 37009 | 0 | 3282 | 755 | 3671 | 1853 | 85360 |
| G33 | 4837 | 220 | 197 | 4013 | 118 | 226 | 8435 | 3282 | 0 | 46 | 558 | 382 | 22316 |
| G41 | 16958 | 1375 | 175 | 1748 | 857 | 372 | 3648 | 755 | 46 | 0 | 448 | 501 | 26882 |
| G42 | 11407 | 1521 | 561 | 5233 | 314 | 774 | 13332 | 3671 | 558 | 448 | 0 | 2252 | 40070 |
| G43 | 5747 | 566 | 853 | 2960 | 96 | 339 | 3444 | 1853 | 382 | 501 | 2252 | 0 | 18994 |
| Sum | 224073 | 38751 | 23742 | 227336 | 49003 | 36275 | 207199 | 85360 | 22316 | 26882 | 40070 | 18994 | 1000000 |
We assume the existence of an unknown trade distance \(D_{ij}\) which summarize tha various factor explains why the observed flows \(F_{ij}\) are not equal to the ones estimated by our double contraint random model \(F^*_{ij}\). Therefore we have the equation :
\(F_{ij} = \frac{a_i.O_i.b_j.D_j}{D^2_{ij}}+\epsilon_{ij} <=> D_{ij} = \sqrt{\frac{F_{ij}}{F^*_{ij}}}\)
Usong the results of our random model we obtain the followig matrix of distance where we have adjust the distances to obtain a maximum of 20000 which is the maximum possible distance on the Earth between two points.
| G11 | G12 | G13 | G21 | G22 | G23 | G31 | G32 | G33 | G41 | G42 | G43 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| G11 | 0 | 3723 | 4189 | 6283 | 8692 | 5263 | 6646 | 6783 | 6296 | 3698 | 5537 | 5321 |
| G12 | 3723 | 0 | 7796 | 8046 | 20000 | 7141 | 9936 | 11047 | 10863 | 4779 | 5580 | 6239 |
| G13 | 4189 | 7796 | 0 | 7063 | 17754 | 6177 | 6762 | 8449 | 8926 | 10415 | 7144 | 3952 |
| G21 | 6283 | 8046 | 7063 | 0 | 3613 | 4948 | 5554 | 6563 | 6986 | 11642 | 8263 | 7494 |
| G22 | 8692 | 20000 | 17754 | 3613 | 0 | 4710 | 9028 | 13779 | 16759 | 6839 | 13876 | 17117 |
| G23 | 5263 | 7141 | 6177 | 4948 | 4710 | 0 | 7435 | 10313 | 10358 | 8879 | 7560 | 7792 |
| G31 | 6646 | 9936 | 6762 | 5554 | 9028 | 7435 | 0 | 4338 | 4509 | 7540 | 4844 | 6501 |
| G32 | 6783 | 11047 | 8449 | 6563 | 13779 | 10313 | 4338 | 0 | 4270 | 9791 | 5453 | 5235 |
| G33 | 6296 | 10863 | 8926 | 6986 | 16759 | 10358 | 4509 | 4270 | 0 | 19682 | 6940 | 5721 |
| G41 | 3698 | 4779 | 10415 | 11642 | 6839 | 8879 | 7540 | 9791 | 19682 | 0 | 8519 | 5494 |
| G42 | 5537 | 5580 | 7144 | 8263 | 13876 | 7560 | 4844 | 5453 | 6940 | 8519 | 0 | 3183 |
| G43 | 5321 | 6239 | 3952 | 7494 | 17117 | 7792 | 6501 | 5235 | 5721 | 5494 | 3183 | 0 |
We propose now to produce a “map” of the relative position of units by mean of a Multi Dimensional Scaling (MDS) method. We use here the smacof program in the simplest version for a first approach :